On the Study of an Initial Value Problem for a Second Order Differential Equation Set in a Singular Cylindrical Domain
DOI:
https://doi.org/10.5644/SJM.15.01.07Keywords:
Fractional powers of linear operators, Analytic Semigroup, Abstract differential equation, Little H¨older space, Interpolation spacesAbstract
We will investigate an initial value problem for a second order differential equation set in a singular cylindrical domain $\Pi $. The existence, uniqueness and maximal regularity results are obtained for the classical solutions by using the semigroup theory. The study is performed in the framework of little Hölder space $h^{2\sigma }(\Pi )$ with $\mathit{0<2}\sigma <1$.
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